List of top Mathematics Questions on Continuity asked in UP Board XII

Prove that the function \( f(x) = |x| \), is continuous at \( x = 0 \).

Prove that the function \[ f(x) = \begin{cases} x^3 - 3 & \text{if } x \leq 2 \\ x^2 + 1 & \text{if } x>2 \end{cases} \] is continuous at \( x = 2 \).